A SHARPE 15.4 GOLD MINING STOCK STRATEGY

Ladies and Gentlemen,

James Simons the mathematician co-responsible for the Chern-Simons invariants (integral of AdA + 2/3 A^3 for connection A on a compact three-manifold that Witten related to Jones polynomials of knots etc.) suggests that the discoveries by the researchers at Renaissance Technologies of anomalies in markets are not worth publishing because they lack universality. Of course universality in science is actually pretty rare as well. Big Bang theory is hardly based on universal features and shares much more with the messy quantitative analysis of financial markets. Anyway, let’s dig into an anomaly of a type that is extremely well-known. You will learn how such a well-known type of anomaly does not disappear. The efficient markets hypothesis is obviously a VERY rough approximation of the truth. The laws of the markets may remain far more mysterious than the laws of the cosmos (whose mysteries in principle can be vastly lowered by removing the Big Bang cosmology and adopting Einstein static universe in principle). The issue at hand is pairs trading on gold companies. The first idea that occurs is that there is a gold mining index ETF and maybe trading components versus the index could be useful. So here is the funny thing. THIS idea does not do very well. So for this idea, ARBITRAGE traders (at D E Shaw, Renaissance etc.) have cleaned up this part. On the other hand a minor variation which I present here will be enormously profitable. The variation is to use the index not for trading but to pick pairs. Use 30-days to calculate CORRELATIONS between the components and the index. Pick two: MAXIMUM correlated and MINIMUM correlated with the GDX index. Then take position on the difference of the two stocks for a single day every day. More precisely, run the following R code which gets the data, runs the strategy etc. The Sharpe is 15.4 on S&P 500. So this strategy is worth investing in by any respectable quant fund (who are reasonably happy to run Sharpe 4+). But what this is telling us is that ARBITRAGEURS are UNABLE to close the gaps of this type which are ALREADY the focus of a great deal of attention. In other words, EFFICIENT MARKET HYPOTHESIS is much like the HUMAN RATIONALITY HYPOTHESIS. It’s extremely misleading. Just as in the Enlightenment there was a hope of human rationality becoming transcendent in some way which then led to not much since rationality of human beings is limited and ultimately not worth centralizing at all, so the EFFICIENT MARKETS HYPOTHESIS is pure dogma. So without further ado, the code and the graph of the backtest. The function cstrat2 with parameters thresh=0.0,holding days=1,number of days to calculate correlations=30 produces the results. There is no cheating (in terms of hidden look-ahead type error) obviously although it’s not trivial to catch such bugs. This is a real (backtest) result which could be implemented live. The interesting issue is precisely the issue of efficient market hypothesis. So how long have people been doing arbitrage with PAIRS? Well, say from the late 1970s. So in principle PAIRS should not produce ANY profits especially when the conglomerate (gold mining stocks) has been of interest for a long time. And yet, a simple variation of basic pairs STILL produces without great deal of sophistication, a sizeable arbitrage opportunity. I am tempted to conclude that the human capacity for ARBITRAGE is much more limited than is justified by the efficient markets hypotheses.